Musicals as an art form have a unique problem. For musical fans, it merely falls under Willing Suspension of Disbelief. For those who dislike musicals, it tends to at least superficially be the reason why.
What's with all the singing?
As we all know, music needs to be composed in advance. Rhyming poetry takes time to piece together. People don't just burst into song and dance in the middle of the street to express their feelings. So how do you make sense of a work of fiction where they do?
The Alternate Universe Hypothesis: The musical is set in an alternate world, or magic has been worked on the ordinary world, in which people really do burst into spontaneous song and dance. If the world has always been this way, singing is simply a normal and commonplace form of human communication, if one that seems a bit odd to those of us living in a less musical world. If the world is not normally this way, expect it to be some sort of an uncontrollable compulsion to sing at emotional moments, sometimes to the extent of summoning a Flash Mob of backup dancers from seemingly nowhere. Sometimes the spontaneous singing is due to the actions of The Music Meister. Characters may here comment explicitly on when they or other characters are singing as opposed to talking (though where the verb "sing" is just used instead of something like "say" in a song, it does not necessarily imply this). This tends to be the most common, especially in stage musicals.
The All In Their Heads Hypothesis: There is no singing; the songs are an artistic rendering of the characters' fantasies, with the format of song in a way serving to distinguish between what really happens and what is only in the characters' heads, much like a ShakespeareanSoliloquy. Naturally, this means that no characters are aware of what goes on in another character's song: there may be duets, but then they are DistantCounterpoint Duets where the two characters do not know of one another's participation.
The Diegetic Hypothesis: The characters are performing actual songs for one another as they might in Real Life, the songs having been written and practiced beforehand in a realistic way. It does not count if the song is merely background music for a scene; if the performance is shown in full and given the viewer's full attention, however, it can count as an example even if the work is not what one would traditionally call a musical. Can overlap with Alternate Universe if writing and performing a song is treated as analogous to writing and giving a speech.
The Adaptation Hypothesis: Derives from the Literary Agent Hypothesis: the songs are merely a dramatic reconstruction of what really happened. For instance, if two characters converse in song and come to some sort of conclusion, it is assumed that the characters really just had a normal, non-musical conversation that came to the same conclusion, but for the sake of upping the drama (or comedy), it has here been adapted into a song. Technically, all musicals are really examples of the Adaptation Hypothesis: there is a story and the music is added to dramatize it. However, to truly count as a definite Adaptation Hypothesis example, the others must generally be clearly not applicable: it must be a non-diegetic song during which the singing character clearly communicates with other characters in some form but the universe is still not implied to treat spontaneous singing as normal.
Of course, musicals rarely consistently adopt one musical world hypothesis for their entirety: most of the time individual songs employ different hypotheses, with some songs even split into sections that seem to use different ones. It is especially common for All In Their Heads songs to be scattered among other songs that are clearly heard by other characters. This makes a degree of sense-after all, in an alternate universe hypothesis musical, an all in their heads song would be the equivalent of an internal monologue in a standard play.
One should also remember that most stories in any genre will contain conceits and set-pieces in order to form a more rewarding narrative. After all, why are there so many snappy one-liners and pratfalls in a comedy? Or why are there so many explosions and car chases in an action movie? Answer: because they just wouldn't be comedy or action movies without them. Musicals have songs in them: just go with it.
Because this trope is a lump, all musicals are technically examples. When adding one, it is therefore necessary to detail which musical world hypothesis applies to which songs.
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The ballet in Princess Tutu is clearly diegetic (except in Dream Sequences, of course). The advanced ballet students show off dances that they've presumably been rehearsing or might have performed in the past, and the bad dancers dance poorly unless they have good partners (in which case they still dance poorly, but at least they look good doing it). Tutu and Kraehe presumably know every dance ever due to their magicalness.
Scott Pilgrim is a strange case. The comics have it as a straight AU example, and is the least weird thing about the universe (which includes universities in the sky, glowing heads, power-ups, 1-ups, magical/vegan powers). The film, on the other hand, treats Matthew Patel bursting into song as very strange even for the universe (as evidenced by Stacey's "what the fuck?" expression)
The League of Extraordinary Gentlemen takes place in a universe where every work of fiction is true (poems and musicals being no exception), so this naturally comes up at one point. In one section of "The New Travelers' Almanac" in the second volume, we learn that the events of Lewis Carroll's poem The Hunting of the Snark were just a hallucination that unfolded in the mind of one Dr. Eric Bellman, a psychiatrist who went insane after trying to lead an expedition into Wonderland. The dialogue in that poem is said to be in verse because Bellman's deteriorating mental state left him incapable of speaking in coherent prose.
In the Century trilogy, however, it's shown that in this world people really do, occasionally, just break into song and everybody treats it like it's normal. It happens several times in 1910, thanks to being a partial adaptation of the Threepenny Opera. In 2009 Alan tries to start a duet with Mina but she's not in the mood. 1969 also has plenty of singing, but it doesn't really count as all of it takes place during rock concerts.
One issue of the Nodwick print comic runs on Alternate Universe (magic influence subtype) rules when Yeagar asks Artax for some magical help to make him more eloquent. Turns out the scroll Artax used made everyone burst into song and dance around Yeagar at the drop of a hat, instead. (Mostly rock and pop parodies from the 80s and early 90s.)
Rent is mostly Alternate Universe with some All In Their Heads (e.g. Without You and What You Own). There are a few diegetic numbers, though, such as "Your Eyes" and "Over The Moon".
Sweeney Todd: The Demon Barber of Fleet Street is also largely Alternate Universe with some All In Their Heads (e.g. Sweeney's portion of Johanna (Reprise), part of Epiphany) and a couple of seemingly diegetic (Toby's 'advertising jingles' first for Pirelli and then Mrs. Lovett's pie shop and the "Parlor Songs" sequence).
Muppet Treasure Island is a mixture, but mostly Alternate Universe combined with a removable fourth wall. It's usually acknowledged that they're singing ("Sailing for Adventure" features Samuel Arrow cautioning them not to get sloppy just because they're singing) but no one seems to find anything strange about it.
"Professional Pirate" is Diegetic, since Long John Silver tells his men to "show 'em you've been practicing".
"Cabin Fever" seems to be All In Their Heads, but only because the crew's been driven temporarily insane. Or was it? Maybe the insanity is what got them all singing about it? The question is never answered.
The Muppets is a blend of Diegetic (mainly near the end, during the fundraiser) and Alternate Universe (The reprise of "Life's a Happy Song" ends with the crowd collapsing from exhaustion; the muppets are baffled by Tex Richman's rap).
Walk the Line is Diegetic, as Johnny Cash is a professional singer on tour with his group. Each musical number depicted in the film occurs at a point that is professionally or personally important to Johnny Cash' life. (For example, his first audition, his first public performance, his comeback performance, asking June to marry him on stage, etc.)
The film version of Chicago falls under All In Their Heads. Except for those numbers actually performed on stage, all the songs are the product of Roxie Hart's imagination, to the point where the song "Class" was removed because there was no way the director could make it fit.
Nine is done by the same director, and does the same thing. Since it's an adaptation of 8 1/2, this works pretty well.
Enchanted is definitely of the Alternate Universe type. Giselle is from another universe and sometimes has the ability to make our universe act according to her universe's rules. When everyone starts singing in Central Park, Robert wonders where they learned the song.
The Wedding Singer is of the Diegetic type. Most of the songs are performed by Robbie in his professional capacity. The only other one is when he is trying to win back Julia; many people in Real Life sing when courting a woman.
Many people refuse to count O Brother, Where Art Thou? as a musical because the songs don't come out of nowhere, but it would fit pretty easily as a diegetic musical.
The Blues Brothers is mostly diagetic, with actually bands and musicians doing rehearsed performances. But then you have Aretha Franklin randomly bursting into song in a diner accompanied by background singers, and people flooding the streets to do a choreographed dance when Ray Charles belts out a number.
The Producers seems to use every version of this in theirs. They are trying to produce a musical so some of the numbers are deliberately rehearsed, others take place in the real world but don't seem to be acknowledged as such, in fact, some of these have to be Adaptation Hypothesis because its only in a later "real world" number that Bialystock notices his co-producer's singing voice.
Once is pretty clearly a Diegetic musical, as the characters are both musicians performing songs for each other and recording an album together, but many of the songs have lyrics relevant to the plot.
Mamma Mia! combines Alternate Universe with Diegetic, as several of the songs are either Donna and her friends reprising their old hits, or Donna's friends reprising their old standards to cheer her up.
Fame (1980) is mostly diegetic, as is appropriate for a film about a school for the performing arts, but one number, Hot Lunch, seems to spill into Alternate Universe territory. An impromptu bit of music by a few students in the cafeteria gradually enlarges to encompass the entire school, spilling out into the surrounding city streets until it literally stops traffic. Somewhat justified, perhaps, in that it is a school for the performing arts, whose student body might be better prepared for sudden improv than your average high school.
Pennies from Heaven (1978 TV miniseries and 1981 Film) -the many lip-synced musical numbers are all in the heads of the main characters.
Monty Python and the Holy Grail is mostly diegetic. The minstrel and his band are clearly singing in-universe about Brave Sir Robin. The Knights Of The Round Table song may appear to be something else, but as part of the song is about how they like to dress up, sing and dance, it's clear that the knights actually are singing and dancing. Which is why Arthur decides not to go to Camelot, as it is "a silly place." The Swamp Castle scenes are probably Alternate Universe, since music will start out of nowhere when Prince Herbert wants to sing, but stops when the King tells it to.
The Mask is an alternate universe example. A little magic from the title character can make people break out in Spontaneous Song And Dance. In fact, people struggle to maintain control as they're forced slowly forced to sing.
The short film 7:35 in the Morning is a diegetic example, and arguably a deconstruction. A woman stopping at a diner is surprised when everyone starts singing to her. As it turns out, a single person wrote the whole song in an attempt to woo her... and he's threatening to blow up the diner if anyone doesn't sing along.
The film version of Cabaret is diegetic. All the songs take place in a night club, with the single exception of "Tomorrow Belongs To Me", a patriotic song that a boy sings to a luncheon, with the diners joining in for the last chorus.
In Dancer in the Dark, all the musical numbers are explicitly depicted as daydreams of the main character, who as it happens loves movie musicals.
Across the Universe combines most if not all of these types, sometimes switching from one to another mid-song; for example, "I Am the Walrus" starts out diagetic, with Bono singing a song for his party guests, and then quickly dissolves into All In Their Heads as the hallucinogens kick in...
Labyrinth is primarily Alternate Universe ("As the World Falls Down" is partially All In Their Heads). All the song-and-dance numbers take place in the Magical Land the heroine is swept into, and unlike most musicals, aren't spread out among the primary characters. A Wacky Wayside Tribe gets one and the primary villain gets the other three, suggesting that singing is simply a way they express themselves.
Singin' in the Rain is almost entirely Alternate Universe, despite being about making a movie musical. The only exception is "Would You?"
This gets pretty complicated when Kathy sings "Singin' in the Rain" at the end of the movie, and everyone, including the orchestra and Lina, knows it already. Up to this point, the song seemed to be either in Don's head or part of the Alternate Universe, but here it becomes more Diegetic. The stage musical version fixes this by having Kathy/Lina sing "Would You?" again, making the show fully Alternate Universe, apart from that one song.
The Nightmare Before Christmas could be either Alternate Universe or Adaptation for most of the movie; it could plausibly be normal for the people of the holiday towns to express themselves by singing (at no point does anyone from the human world sing) but no one ever comments on it. Exceptions:
"This Is Halloween" is pretty clearly Diegetic, since the citizens of Halloweentown plan a big event every Halloween, and the way the Mayor walks up to Jack's doorstep humming the tune the next day points toward the characters at least knowing the song in-universe.
"What's This?" cannot possibly be anything other than All In Their Heads, because even though Jack's running around singing and making a spectacle of himself, the only time anyone even comes close to noticing him is when he passes within a hair's breadth of them.
"Poor Jack" could be All In Jack's Head, or it could be out loud, because Jack is the only one around at the time; he could be talking/singing to himself, or just having an inner monologue.
"Sally's Song" is similar, but she does walk past some street musicians who don't react. This might mean it's all in her head, or it might mean that they don't care.
The 2005 adaptation of Charlie and the Chocolate Factory is purely Diegetic, with the first song sung by Wonka's automatons and the rest sung by Oompa-Loompas. This trope is actually discussed in the movie, and Wonka claims that the Oompa-Loompas' songs are improvised on the spot... except they clearly aren't. Naturally, this led to fan theories that they rehearsed the songs beforehand and Wonka specifically picked the route that would make the spoiled children's presumed flaws manifest.
Hairspray is a mixture of Alternate Universe and Diegetic, with one or two songs that might possibly be All In Her Head.
Pitch Perfect is firmly Digetic. The Bellas are shown practice their choreography and harmonizing. When Beca sings another song during Semi Finals, Aubrey calls her out for breaking from routine. During the Riff-Off, some songs seem to practiced or familiar, while some of the songs are done with the singers "improving".
Repo: The Genetic Opera has almost no spoken dialogue, being an opera (or a rock opera, at least). Most of the movie is Alternate Universe, but it gets a little mixed up when they actually get to the Genetic Opera. While Mag and Amber's songs are clearly meant to be Diegetic, "We Started This Op'ra Shit" is a mix (most of the song is meant to be a rehearsed performance, but the single mom's testiominal isn't) and they switch back to Alternate Universe after the Genetic Opera ends (even though the characters are still onstage). "Seventeen" is partly All In Their Heads; while it involves an argument between Shilo and her dad, Shilo also sings it directly into a microphone with a backing band that includes Joan Jett! And Grave Robber is a special case altogether, since half of his songs are exposition sung directly to the audience.
Reefer Madness, the musical, not the early 30's Scare 'Em Straight film, certainly is "All in their heads." The opening song shows the parents beginning to panic over the thought of their children becoming monsters for smoking marijuana. Then their kids become literal ghouls and mob the parents, complete with dance choreography from Michael Jackson's Thriller. At the end of the song, the ghouls vanish and the parents are firmly in the hands of an anti-pot activist. The silliness only goes up from there.
Scott Pilgrim vs. The World is not a musical, but quite a few musical numbers come up and are important to the plot. They are always both diegetic and in an Alternate Universe where the world follows video-game and comic-book like rules. For example, one set of performers tears the roof off the building, meaning they stun the crowd -and- tear the roof clean off the building.
Darling Lili is diegetic. Most of the musical numbers are performances by Lili or other characters. There's also a song (which doesn't appear in the Director's Cut) sung by a group of French schoolchildren whom Lili and Bill follow for a while during their romantic weekend in the country.
Save for two songs that are diegetic (both versions of In The Flesh, where Pink is seen singing in front of an audience), the film version of The Wall is purely adaptational, as is suggested by the opening song, where Pink tells the audience that to see his true self, they have to claw their way through his disguise. Also, several songs, such as "Comfortably Numb" only work in an adaptational sense (in the case of "Comfortably Numb", though singing, Pink admits he can't hear what the doctor is saying, yet he seems to respond to him as if he can). though others, like "The Trial", work best in an all in his head form.
Live Action TV
The Flight of the Conchords TV show is about musicians and thus a lot of the songs are diegetic (e.g. Bret, You've Got It Going On, If You're Into It and Albi the Racist Dragon, the last being on a Show Within a Show). However, other songs are All In Their Heads (e.g. She's So Hot, Boom, which stylistically shows the girl it is sung to during it but is still obviously not actually being performed for her, Business Time, Mermaids, Sugarlumps), and others are clearly Adaptation Hypothesis examples (e.g. Most Beautiful Girl in the Room, Hurt Feelings, I Told You I was Freekie). One of relatively few musicals that are not Alternate Universe at all.
In the Flight of the Conchords song Hiphopopotamus vs. Rhymenoceros (feat. the Hiphopopotamus and the Rhymenoceros), which is All in Their Heads, one of the muggers asks if they 'were dancing a little bit just then'. They say no, sheepishly.
Deconstructed in the Musical Episode of Scrubs, "My Musical," as the singing was a hallucination of a patient who had a stroke, and in fact her life was in danger. When she is cured, it stops, but the episode ends with her humming to herself as she misses the music inside her head. So All In One Character's Head, mixed with the spirit of the Adaptation Hypothesis (characters singing to each other are really having those conversations, but not really singing).
This also causes a bit of Fridge Brilliance to kick in, since the patient isn't around for any of the actual dialogue sequences, and as soon as she does appear, characters break into song, even if they're halfway through a conversation.
The BuffyMusical Episode is an example of the "magic spell" subset of the Alternate Universe Hypothesis. Everyone in Sunnydale starts singing and dancing uncontrollably, as if they're in a musical. They know it's weird, but they can't stop. The culprit turns out to be Sweet, a demon that Xander accidentally summoned. It makes people sing about their hidden feelings, causing various relationship problems, and in some extreme cases the people with the biggest secrets dance until they literally burn up.
Interestingly, something of a variant in that the characters often seem only half-aware of the content of one another's songs - most prominently when Buffy completely fails to notice that Giles, in the room with her, is singing a lament about how he is standing in her way ("Did you just say something?"), but also for instance when Xander and Anya complete a song about not telling each other about their flaws and concerns about their upcoming marriage and only afterwards seem to realize that they just told one another anyway.
Nah, Buffy just wasn't paying attention
Giles: I've got a theory, that it's a demon. A dancing demon! No, something isn't right there
Willow: I've got a theory, some kid is dreaming, and we're all stuck inside his wacky broadway nightmare!
Xander: I've got a theory we should work this out
All: It's getting eerie... What's this cheery singing all about?
The truth is I never left you All through my wild days My mad existence I kept my promise Don't keep your distance.
Juan Peron: What the hell was that? Eva Peron: What was what? Juan Peron: You were singing. Eva Peron: Oh.. I, I, I did, didn't I? Juan Peron: Yeah, yeah, don't do that!
One of Alex Borstein's characters on MADtv was a redhead named Annie whose spontaneous musical outbursts were stated to be a stress-triggered mental illness.
Glee seems to primarily be diegetic, but mixes in a decent sprinkle of "All in Their Heads", numbers. Also, it doesn't do to think too hard about the quality of some of the first read-throughs from a purely diegetic perspective.
Even Stevens' "Influenza: The Musical" is a combination of Alternate Universe and All In Their Head. Specifically, Ren's.
That's So Raven had a diegetic musical episode, wherein all the wacky antics are supposed to wow a talent scout disguised as a janitor.
Pennies from Heaven (1978 TV miniseries and 1981 Film) -the many lip-synced musical numbers are all in the heads of the man characters.
Dennis Potter LOVED this trope - also seen in Lipstick On Your Collar, used in exactly the same way as in Pennies.
The musical episode of Sanctuary is an interesting variation. Abby is singing (without realizing it) to other characters because she's been infected with a parasite that interferes with processing and producing normal speech. Everyone else sings to Abby out of necessity since she can't understand them otherwise. The songs are not rehearsed and are basically just sung dialogue.
One Saturday Night Live skit, Zac Efron plays his signature character, the star of the High School Musical series, giving a speech to his former classmates after he'd spent a year at college. He crushes their illusions (and lack of Medium Awareness) by explaining that the music seems to stop after graduation, and spontaneous singing just gets you funny looks. (So it's the alternate universe interpretation combined with Like Reality Unless Noted.)
"And from what I can tell, this is America’s only singing high school! I was as shocked as you are."
The Musical Episode "The Gunfighters" mostly has a variant of All In Their Heads, as the songs act as a Greek Chorus, communicating on the action without actually engaging in it. However, there is a big diagetic musical number when Steven and Dodo, and later Steven and Doc Holiday's girlfriend, are forced by a bunch of gangsters to sing in order to prove that they really are a group of travelling singers and therefore aren't in league with Doc Holiday.
The audio drama "Dr Who and the Pirates" is a weird blend of all of these. The story is presented as a tale that Evelyn is telling someone else, but when the Doctor cuts in he decides to improve it by making it into a musical, with him singing (and Evelyn being very embarrassed by this) - an in-universe Adaptation. Yet the songs we hear in the story are presumably being performed by the Doctor in the 'real world' - Diagetic - though without the backing music or singers we hear - which are All In His Head. Also, within the world of the story itself, just bursting into song is considered normal by the minor pirate characters - Alternate Universe.
The first half of Mad Men's last season ends with Bert Cooper performing "The Best Things in Life Are Free" for Don with several unknown women. Considering all the performers disappeared the second it ended, no one reacted to it except Don, and Cooper had just died earlier than day, this falls pretty clearly in "All In Their Head".
The movie adaptation, however, mixes in some "All In Their Heads" numbers - "Wig in a Box" is a flashback to an epiphany conveyed as a musical number, and the final four numbers ("Hedwig's Lament," "Exquisite Corpse," "Wicked Little Town" reprise, and especially "Midnight Radio") are presented in a Mind Screw that could be any combination of Diegetic, All In Their Heads, or Adaptation.
The stage version of Cabaret includes a lot of diegetic songs, performances at the Kit Kat Klub, but also a high percentage of songs like "So What" or "It Couldn't Please Me More", which fall under the Alternate Universe distinction.
Despite being set during the casting of a Broadway musical (and thus perfect fodder for the Diegetic), most of the singing in A Chorus Line are either Alternate Universe or All In Their Heads.
Spring Awakening is mostly All in Their Heads for solo numbers, though group songs seem to make use of the Adaptation Hypothesis.
Fiddler on the Roof seems to have most of the categories. Tevye's monologues are clearly All In Their Heads, while his 'Do You Love Me' with Golde fits into Adaptation Hypothesis. Most of the other songs fit into Alternate Universe.
Oliver! is mostly Alternate Universe, though the songs Nancy sings at the Three Cripples Inn ("It's a Fine Life" and "Oom Pah Pah") can fit into Diegetic.
The songs the Hot Box Girls sing in Guys and Dolls are Diegetic, as is the Mission ensemble's 'Follow The Fold', but most of the other songs are either Alternate Universe or Adaptation Hypothesis.
in '1776'', every song John Adams sings with Abigail is All In Their Heads with a bit of Adaptation Hypothesis (as, in actuality, Abigail was back in Massachusetts and could only communicate with John by writing letters. So the instant two-way communication in those scenes only happens in John's mind). The other songs are either Alternate Universe or Adaptation Hypothesis.
Actually, Adaption Hypothesis for the majority of it: 1776 uses as one of its major sources the writings of the people who were there at the time, to the point of reusing actual text with, at most, modernization of the English.
Alternate Universe, however, is also valid given how smoothly Thomson inserts himself into the lyrics of "Cool, Cool, Considerate Men." Clearly, he's used to Congress doing this sort of thing.
The Phantom of the Opera is approximately two-thirds Adaptation/All In Their Head and one-third Diegetic, with the "operas" and a few other examples like "Music of the Night" (which is basically the Phantom attempting to seduce Christine via Villain Love Song) happening as they would in real life but mostly with people singing what they would normally say or think to themselves. The film version supports supports the Adaptation Hypothesis by including scenes where characters actually speak the lyrics rather than sing them (although the result is awkward to say the least).
As the main character in Top Hat is a musical star several songs are diegetic (such as "Top Hat, White Tie and Tails") as part of the various shows he was part of. "Dancing Cheek To Cheek" was an odd example that was simply the character singing lyrics to a song while they were ballroom dancing (two other songs are sung by other in-universe performers). The rest are all part of the Alternative Universe, a character did in fact get in trouble for tap dancing too loudly.
Curtains is largely diegetic, with several songs being rehearsals for the Show Within a Show. Tough Act to Follow has enough dream sequence elements to be All in Their Heads for Cioffi and Nikki, and several other songs are a sort of Alternate Universe, since almost the entire cast is the cast of the Show Within a Show and are therefore ready to perform at the drop of a hat. Of particular note is The Woman's Dead, which Belling declares to be an acting exercise but is too well rehearsed to be such a thing.
Reefer Madness, as mentioned under film, is "All in their heads," though as less theater companies can afford to do the elaborate pieces that were done for the film, at times it may also be Adaptation. Consider Little Mary Sunshine - Showtime's version dives headlong into a theatrical version of a sex dungeon, while most theater companies simply have Mary engage in a little Double Standard: Rape, Female on Male.
Epic Mickey 2: The Power of Two is most likely diegetic. The Mad Doctor is the only character who sings, and the other characters react to it as if it's unusual. However, some other characters join in without any sort of reaction during "Fall of Prescott".
Dr. Horrible's Sing-Along Blog seems to largely use the Alternate Universe Hypothesis plus All In Their Heads, but still a bit of the Adaptation Hypothesis:
Judging from the half-embarrassed way in which Billy stops singing when Moist enters, Freeze Ray seems to imply he really is singing, hence Alternate Universe, though the laundromat scenes are of course All In His Head.
Although it's possible that the part of the song where he sings to Penny and she responds is flashback to something that really happened - he was going through the song in his head but then accidentally sang a line out loud. It never really clarifies what happened there.
Both versions of the Bad Horse Chorus are Adaptation Hypothesis: Billy actually is reading the letter, but the singing cowboys are an artistic touch to make the reading of the letter more fun.
Brand New Day and Everything You Ever are All In Billy's Head, inner monologues that are clearly not heard by the other characters around in the scene.
My Eyes is an All In Their Heads duet, with no other characters present in the scenes being aware of either Billy or Penny's singing.
Caring Hands, A Man's Gotta Do, Penny's Song, and So They Say are all probably Alternate Universe.
Everyone's a Hero and Slipping are probably Adaptation, with Captain Hammer giving an insensitive speech rather than a song, and Doctor Horrible announcing to the crowd his existence as a villain.
Also discussed in the video "The Horrifying Truth About Life Inside Movie Musicals", where they suggest telepathy, puppeteers, slavery, fascism, mental illness, and the idea of singing and dancing providing a drug-like high as in-universe reasons why everybody sings in musicals.
"Zanzibar", the Musical Episode from Rocko's Modern Life, used the Diegetic Hypothesis, where it turns out everyone had actually gone to rehearsals in preparation... everyone except Rocko, who missed the fliers announcing the upcoming musical, and so tends to flounder whenever he tries to sing.
Although weirdly, while the songs were supposed to be rehearsed beforehand, most of the events that they're singing about are supposed to be happening naturally. Lampshaded:
Rocko: Uh...this was sort a...spur-of-the-moment, spontaneous thing.
Security Guard: Uh-huh. And how do y'all know the words?"
The episode "Mayhem of the Music Meister!" of Batman: The Brave and the Bold is the "Alternate Universe with magic" type, as the villain's hypnotic voice caused people to sing and dance under his control. (How everyone knew what they had to sing and do is not explained however. Though the Meister's songs don't have to specify the actual commands (he doesn't say anything like "Attack Batman" during Drives Us Bats, but they do anyway), so he probably mindcontrolled them into knowing the lyrics.)
It's also slightly diagetic- the Music Meister didn't seem to have anything to do with "If Only".
And it's actually Lampshaded by Batman after Death Trap, which Black Canary sang after Music Meister had already left the room.
Batman: Was the singing really neccessary?
It seems that every animated series finds a way to give Joker a musical number. All of them Diegetic, in character, and fit in-scene.
BTAS - Jingle Bells Batman Smells
The Batman - Setting the Woods on Fine
Batman Brave and the Bold - Where's the Fun in That
The ''Veggie Tales: Jonah movie plays with this trope. Jonah's musical number inside the whale seems to be Adaption Hypothesis, but apparently the singing and music are actually taking place as there is a cut to confused fishermen who can vaguely hear the noise coming from underwater, which would make it Alternate World instead.
The Sword in the Stone, for example, most of the singing done by characters with magical powers, and it's easy to imagine them casting spells using music.
Tangled introduces a twist during "I've Got A Dream": In this Alternate Universe, some people choose not to burst into song due to cynicism, grumpiness, or plain ol' bad mood. Flynn is perfectly capable of joining the Crowd Song, but is unwilling to do so until he is forced at swordpoint! In fact, his spontaneous duet with Rapunzel during "I See The Light" is indicative of his character development and shift towards more idealistic values.
Phineas and Ferb is definitely a musical world, although an...interesting one. While people fo burst into song and dance at random times, Doofensmirtz has been known to hire back-up singers specifically for this purpose. Also, the Musical Episode lampshades it to hell and back.
Phineas: Why don't we burst into spontaneous singing and dancing with no discernible music source?
Also, they appear to be able to hear the soundtrack- and their singers. They have, in fact, had arguments with them.
Total Drama World Tour is mostly Digetic (except for the part where they plan songs out in advance); but the visuals, such as a cut to Team Amazon playing in a real band or both teams dancing in jumpsuits, are Adaptions even when they're signing the song in real time.
One could argue that it's a weird mixture of Digetic and Alternate Universe: this is not a world where breaking into song is normal, and the characters explicitly do not prepare in advance or know what their songs will be about. Nevertheless when Chris ordains it, music seems to come out of nowhere and the characters are able to spontaneously singand dance with only an occasional broken rhyme or confused look.
In all the Rugrats movies, only the babies and Angelica (as well as an amnesiac Nigel Thornberry in a Cut Song) break out into musical numbers for no real reason, whereas the adults only sing when they have a reason (trying to sing a baby to sleep, it's part of their job, etc.).
Dr. Lipschitz has a song in the extended cut of The Rugrats Movie, but it's in a dream sequence.
My Little Pony: Friendship Is Magic: Pinkie Pie's solo songs are pretty much all Diegetic (Other characters point out her tendency to burst into song, and she's shown preparing/rehearsing on several occasions), while most of the other songs generally follow the Alternate Universe or Adaptational concepts. "Find a Pet Song" was a completely unrehearsed duet, but was explicitly acknowledged to have been sung in-universe, and multiple characters have made in-universe shout-outs to the ensemble song "Winter Wrap Up", implying that the singing actually happened and is a normal thing for this universe. "This Day Aria", meanwhile, is a Distant Duet, which seems impossible to explain without resorting to the Adaptational view, and many songs (such as "True True Friend") flow across several scenes which could not possibly be taking place at the speed of the song. In the case of "Generosity", Rainbow Dash points out the weirdness of bursting into song randomly, implying it's an unusual thing in this universe, which, considering the earlier examples, makes for a bona fide Mind Screw...which is made even MORE confusing when Rainbow herself seems to reference "The Failure Song" in Testing Testing 1, 2, 3.
Futurama tends to fall into the Alternate Universe version (with the exception of "Don't Worry, Bee Happy", which was explicitly all in Leela's head). Someone in the song will generally lampshade the fact that they're all singing:
Professor:I can't believe the Devil, is so unforgiving! Zoidberg:I can't believe that everyone is just ad-libbing!
And in one episode where Zoidberg has a musical number, Amy is deeply annoyed by the fact that Zoidberg is harmonizing with himself. No one else seems bothered by it, though.